A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds

Question

A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 69 per hour, and this rate is Poisson-distributed.

Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)

Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Determine the average number of customers in the system. (Do not round intermediate calculations.Round your answer to 2 decimal places.)

A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 69 per hour, and this rate is Poisson-distributed.

Explanation / Answer

= 75 69 customers per hour

=60*60/30 = 120 customers per hour

= / = 7/120 = 0.625   69/120=0.575

the average number of customers waiting in line

Ii = 2 / 2(1- ) = 0.5752 / 2(1-0.575) = 0.33/0.8= 0.39 customers

the average time customers spend in the system

Ti = Ii / =0.39/69=0.00565 hours

T = Ti + 1/ =0.00565+1/120=0.01239hours =0.839 minutes

average number of customers in the system

I = Ii + =0.39+0.575 =0.965 customers

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.